Write the slope-intercept form of an equation of the line that passes through (a, - 4) is parallel to the graph of 4x - y = 2 y = - 1/4 * x + 4 y = 1/3 * x - 4 y = 4x - 4 D y = - 4 - 4

Answers

Answer 1

Answer:

The first questionsanswer:

Given (0, -4), 4x - y = 7. I converted the equation into slope intercept form and I got: y = 4x - 7. Once I had gotten that I put (0, -4) and the equation into Point-Slope Form and solved it: y - (-4) = 4(x + 0), y + 4 = 4x, y = 4x - 4 is the slope intercept form of your equation and point :)

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Use a Venn diagram to answer the question. A survey of 180 families showed that 67 had a dog; 52 had a cat; 22 had a dog and a cat; 70 had neither a cat nor a dog, and in addition did not have a parakeet; 4 had a cat, a dog, and a parakeet. How many had a parakeet only?

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 4640 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize the cost. (Round your answers to three decimal places.)

Answers

The dimensions that minimize the cost of building the tank are $r\approx 6.5ft \text{ and } h \approx 26.0ft$ .

Let

$h=\text{the height of the cylindrical sides}\nr=\text{the radius of the hemispheres and the cylindrical sides}$

and

$T=\text{the total cost}\nu_c=\text{the unit cost of building the cylindrical sides}\nu_h=\text{the unit cost of building the hemispherical surfaces}$

and

$S_c=\text{the surface area of the cylinder}\n=2\pi rh\n\nS_h=\text{the total surface area of both hemispheres}\n=4\pi r^2$

Therefore,

$T=u_cSc+u_hSh$

From the question

$u_h=2u_c$

The total cost becomes

$T=u_cSc+2u_cSh\n=2u_c \pi rh+8u_c \pi r^2$

We need to eliminate $h$ . The volume from the question gives a way out

$4640=(4)/(3)\pi r^3 +\pi r^2h\n\nh=(4640)/(\pi r^2)-(4r)/(3)$

substitute into the formula for total cost gives, after simplifying

$T=(16u_c\pi r^2)/(3)+(9280u_c)/(r^2)$

differentiating with respect to $r$ , we get

$(dT)/(dr)=(32)/(3)u_c\pi r-(9280u_c)/(r^2)$

at extrema

$(dT)/(dr)=0\n\n\implies (32)/(3)u_c\pi r=(9280u_c)/(r^2)\n\nr=\sqrt[3]{(870)/(\pi)}\approx 6.5ft$

To confirm that $r$ is a minimum value, carry out the second derivative test

$(d^2T)/(dr^2)=(32u_c\pi)/(3)+(18560)/(r^3)$

substituting $r=\sqrt[3]{(870)/(\pi)}$ , we get that $(d^2T)/(dr^2)$ > $0$ , confirming that minimum value

To find $h$ , recall that

$h=(4640)/(\pi r^2)-(4r)/(3)$

substituting $r$ , we get $h\approx 26.0ft$ as the corresponding minimum height

Therefore, $r\approx 6.5ft \text{ and } h \approx 26.0ft$ minimize the total cost of building the tank.

Learn more about minimizing dimensions to reduce costs here: brainly.com/question/19053049

Final answer:

The problem involves finding the dimensions of a cylinder and two hemispheres that minimize the cost to build an industrial tank of a specific volume. This involves setting up equations for the volume and cost, and then using calculus to find the dimensions that minimize the cost.

Explanation:

This problem can be solved using calculus. Let's denote the radius of both the hemispheres and the cylinder as r and the height of the cylinder as h. The total volume of the solid is the sum of the volume of the cylinder and the two hemispheres. Using the formulas for the volumes of a cylinder and hemisphere, we have:

V = (πr²h) + 2*(2/3πr³) = 4640 cubic feet.

The total cost of the material is proportional to the surface area. The surface area of the two hemispheres is twice as expensive as that of the sides of the cylinder, so we have:

Cost = 2*(2πr²) + πrh.

To minimize the cost, we can take the derivative of the Cost function with respect to r and h, set them equal to zero, and solve for r and h.

This problem involves calculus, the volume of cylinders and spheres, and optimization, which are topics covered in high school mathematics.

Learn more about Mathematics Optimization Problems here:

brainly.com/question/32199704

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Ice cream sales and the number of shark attacks have a positive correlation. The conclusion that eating ice cream causes shark attacks is A) justifiable, because the milk in ice cream attracts sharks. B) justifiable, because a positive correlation implies causation. C) not justifiable, because a positive correlation negates causation. D) not justifiable, because ice cream sales and shark attacks both rise during the summer.

Answers

Answer: D)not justifiable, because ice cream sales and shark attacks both rise during the summer.

Step-by-step explanation:

Correlation: It indicates that there is relation between any two variablesor more than two variable.

Causation: It is a type of correlation where one variable if affects other variable directly.

Thus , Causation implies correlation.

But correlation does not imply causation.

Therefore, if there is a positive correlation between ice cream sales and shark attacks , then we can not say there is a causation as both are not linked directly.

Hence, the statement is not justifiable, because Ice cream sales and shark attacks both rise during the summer and both are not interlinked.

I think that must be D

Triangle EFG is graphed below. If the triangle is translated 4 units to the right and 3 units down, what will be the coordinates of G’ ? A. (3,-2) B. (3,4) C. (2, -3) D. (2,2)

Answers

Answer:

A) (3,-2)

Step-by-step explanation:

A) (3,-2)

Need help please badly

Answers

Answer:

CED is a right angle, CEB=AEB

hopw that helps

Answer:

1st, 2nd, 5th

Step-by-step explanation:

how many pounds of chamomile tea that costs 18.20 per pound must be mixed with 12lb of orange tea that costs 12.25 per pound to make a mixture that costs 14.63 per pound

Answers

8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.

Step-by-step explanation:

We are given the following in the question:

Chamomile tea:

Unit cost = 18.20 per pound

Amount = x pounds

Total cost =

$18.20* x = 18.20x$

Orange tea:

Unit cost = 12.25 per pound

Amount = 12 pounds

Total cost =

$12.25* 12 = 147$

Total mixture:

Unit cost = 14.63 per pound

Amount = (12+x) pounds

Total cost =

$14.63* (12+x) = 175.56 + 14.63x$

We can write the equation that cost of mixture is equal to cost of chamomile tea and orange tea.

$18.20x + 147 = 175.56 + 14.63x\n\Rightarrow 18.20x- 14.63x = 175.56-147\n\Rightarrow 3.57x = 28.56\n\Rightarrow x = 8$

Thus, 8 pounds of chamomile tea must be mixed to make a mixture that costs 14.63 per pound.

You and your friend enter frogs in a frog-jumping contest. Your friend’s frog jumps 14 feet. Your frog jumps 16 feet. How much farther does your frog jump? 2 7/12
2 5/12 feet
1 7/12
1 5/12 feet

Answers

Answer: 2 feet.

Step-by-step explanation: 16 - 14 = 2. That would be 14 inches. 2 feet.

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