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Please help me thank you

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

b = a^2/4 +4

Let a =8

b = 8^2 /4 +4

= 64/4 +4

= 16 +4

= 20

Answer 2

Answer:

Answer:

b = 20 when a = 8.

Step-by-step explanation:

For this problem, we will simply plug the value of a=8 into the given equation for b, to find the value of b.

b = [ (a)^2 / 4 ] + 4

b = [ (8)^2 / 4 ] + 4

b = [ 64 / 4 ] + 4

b = [ 16 ] + 4

b = 20

Hence, when the value of a=8, then the value of b=20.

Cheers.

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Find the indefinite integral using the substitution x = 10 sin(θ). (Use C for the constant of integration.) 1 (100 − x2)3/2 dx

Answers

Answer:

The indefinite integral

= $(1)/(100)$ ˣ $\frac{x}{\sqrt{100-x^(2) } }$ ⁺ C

Step-by-step explanation:

x= 10sinθ

dx = 10cosθdθ

the step-to-step explanation is in the attachment

Final answer:

We solve the given integral using substitution and the trigonometric identity. The answer to the integral, after substitution and simplification, is x/10 + C, where C is the integration constant.

Explanation:

To solve the integral problem given, ´∫ 1/(100 − x²)^(3/2) dx´, we will apply the substitution method, which is a common technique in calculus. Here we are using the substitution x = 10 sin(θ) .

Firstly, substituting for x, we get dx/dθ = 10 cos(θ) or dx = 10 cos(θ) dθ. The integral becomes ∫ 10 cos(θ)/ (100 − 100sin²(θ))^(3/2) dθ = ∫ cos(θ) dθ. The indefinite integral of cos(θ) is sin(θ).

Re-substituting x = 10 sin(θ) back into the equation we get sin(θ) = x/10. Thus, the indefinite integral is x/10 + C. Here C is the constant of integration.

Learn more about Integration here:

brainly.com/question/34630729

#SPJ3

A bank credit card charges interest at the rate of 24% per year, compounded monthly. If a senior in college charges $1,500 to pay for college expenses, and intends to pay it in one yewhat will he have to pay? (Round your answer to the nearest cent.)

$

Answers

Answer: 1902.36

Step-by-step explanation:

When interest is compounded monthly , the formula to find the accumulated amount is

$A=P(1+(r)/(12))^(12t)$ , where P = principal value , r = rate of interest , t = time.

As per given,

r= 24% = 0.24

P= $1500

t= 1 year

Put all value in formula , we get

$A= 1500(1+(0.24)/(12))^(12* 1)\n\n=1500(1+0.02)^(12)\n\n=1500(1.02)^(12)\n\n=1500(1.26824179456)\approx1902.36$

Hence, he need to pay $1902.36.

A rectangle with an area of 324 square meters has a length and width in a ratio of 4:1. What are the length and width?

Answers

Here, 4x * x = 324
Now, we need to calculate that unit of x value as follows:
4x * x = 324
4x² = 324
x² = 324/4
x² = 81
x = √81
x = 9
So, 4x = 4(9) = 36

So, dimensions of rectangle would be: 36 × 9

Hope this helps!

HELP FATS PLEASE
WILL MARK BRAINLEYST
HOW TO STEP BY STEP SOLVE THIS

Answers

Answer:

Step-by-step explanation:

(y+2)'2-5=20

(y+2)'2=15

y·y+4=15

y·y=11

y=11y

y=5.5

What’s the answer to this

Answers

answer : x-intercept = (11,0)
y-intercept = (0,6)

Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p 1 be the proportion of customer complaints with the old dough and p 2 be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough g

Answers

Answer:

$z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)((1)/(385)+(1)/(340))}}=-2.469$

Now we can calculate the p value with this probability:

$p_v =P(Z<-2.469)= 0.0068$

Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.

Step-by-step explanation:

Information provided

$X_(1)=6$ represent the complaints with the old dough

$X_(2)=16$ represent the complaints with the new dough

$n_(1)=385$ sample 1 selected

$n_(2)=340$ sample 2 selected

$p_(1)=(6)/(385)=0.0156$ represent the proportion of complaints with the old dough

$p_(2)=(16)/(340)=0.0471$ represent the proportion of complaints with the new dough

$\hat p$ represent the pooled estimate of p

z would represent the statistic

$p_v$ represent the value

Hypothesis to test

We want to verify if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough, the system of hypothesis would be:

Null hypothesis: $p_(1) \geq p_(2)$