A ladder leans against a building that angle of elevation of the latter is 70° the top of the ladder is 25 feet from the ground. to the nearest 10th of a foot how far from the building is the base of the ladder a. 20.5 feet b. 30.5 feet C.32.3’ or D.39.5 feet

Answers

Answer 1

Answer:

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

Answer 2

Answer:

Answer:

The correct answer option is a. 20.5 feet.

Step-by-step explanation:

We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.

We are to find the distance of the building from the base of the ladder.

For this, we will use tan:

$tan 70 = \frac { 2 5 } { x }$

$x = \frac { 2 5 } { tan 7 0 }$

x = 20.5 feet

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Y+z+ 2; use y=-6, and z = 5

Answers

When y = -6 and z = 5, the value of the expression y + z + 2 is 1.

To calculate the expression y + z + 2 when y = -6 and z = 5, you simply substitute these values into the expression and perform the arithmetic operations:

y + z + 2 = (-6) + (5) + 2

Now, perform the addition:

(-6) + (5) + 2 = -1 + 2 = 1

So, when y = -6 and z = 5, the value of the expression y + z + 2 is 1.

for such more question on expression

brainly.com/question/4344214

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Answer:

Step-by-step explanation:

y + z + 2

first you have to replace the variables with the numbers

This is your equation now.

-6 + 5 + 2

Now you just have to solve it.

-6 + 5 = -1+ 2 = 1

7 - 6 = 1

Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8

Answers

Answer: The required equation of the ellipse in standard form is $(y^2)/(25)+(x^2)/(16)=1.$

Step-by-step explanation: We are given to find the equation of an ellipse in standard form with the vertical major axis of length 10 units and minor axis of length 8 units.

Since the major axis is vertical, so it will lie on the Y-axis. Let the standard form of the ellipse be given by

$(y^2)/(a^2)+(x^2)/(b^2)=1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where the length of major axis is 2a units and length of minor axis is 2b units.

According to the given information, we have

$2a=10\n\n\Rightarrow a=(10)/(2)\n\n\Rightarrow a=5$

and

$2b=8\n\n\Rightarrow b=(8)/(2)\n\n\Rightarrow b=4$

Substituting the values of a and b in equation (i), we get

$(y^2)/(5^2)+(x^2)/(4^2)=1\n\n\n\Rightarrow (y^2)/(25)+(x^2)/(16)=1.$

Thus, the required equation of the ellipse in standard form is $(y^2)/(25)+(x^2)/(16)=1.$

(x/h)^2+(y/v)^2=1 where h is the horizontal radius and v is the vertical radius

In this question it seem that they are saying the length of the axis and not radius so I would cut them in half so that they are radii...then:

(x/4)^2+(y/5)^2=1

x^2/16+y^2/25=1

Let a1equals[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix ], a2equals[Start 3 By 1 Matrix 1st Row 1st Column negative 7 2nd Row 1st Column negative 7 3rd Row 1st Column 2 EndMatrix ], and bequals[Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 22 3rd Row 1st Column h EndMatrix ]. For what value(s) of h is b in the plane spanned by a1 and a2?

Answers

Answer:

For h= 25, b in the plane spanned by a1 and a2

Step-by-step explanation:

$a1= \left[\begin{array}{c}1\n2\n-1\end{array}\right] \na2 = \left[\begin{array}{c}-7\n-7\n2\end{array}\right] \n\nb = \left[\begin{array}{c}3\n-22\nh\end{array}\right]$

we have to find value of h for which b in the plane spanned by a1 and a2.

For this the linear systems given by the following augmented matrix must be consistent.

$\left[\begin{array}{cc|c}1&-7&3\n2&-7&-22\n-1&2&h\end{array}\right]$

Reduce the augmented matrix into row echelon form:

$R_(2) - 2R_(1) , R_(3) + R_(1)\n\n\left[\begin{array}{cc|c}1&-7&3\n0&7&-28\n-0&-5&h+3\end{array}\right]\n\n7R_(3)+5R_(2)\n\n\left[\begin{array}{cc|c}1&-7&3\n0&7&-28\n-0&0&7h-175\end{array}\right]$