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insens350 [35]
3 years ago
14

Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.

Mathematics
1 answer:
o-na [289]3 years ago
3 0
Use the pythagorean theorem,
a^2+b^2=c^2
1^2+1^2=c^2
1+1=c^2
2=c^2
2=2
Square root of 2 is 1.41 (approximately)
c=1.41
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murzikaleks [220]

Answer:

x-4y+4=0

f(x)=\sqrt x and x=4

Step-by-step explanation:

We are given that a curve

y=\sqrt x

We have to find the equation of tangent at point (4,2) on the given curve.

Let y=f(x)

Differentiate w.r.t x

f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}

By using the formula \frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}

Substitute x=4

Slope of tangent

m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}

In given question

m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}

\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}

By comparing we get a=4

Point-slope form

y-y_1=m(x-x_1)

Using the formula

The equation of tangent at point (4,2)

y-2=\frac{1}{4}(x-4)

4y-8=x-4

x-4y-4+8=0

x-4y+4=0

8 0
3 years ago
The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a n
xz_007 [3.2K]

Answer:

(15,595, 16,805)

Step-by-step explanation:

We have to:

m = 16.2, sd = 3.75, n = 150

m is the mean, sd is the standard deviation and n is the sample size.

the degree of freedom would be:

n - 1 = 150 - 1 = 149

df = 149

at 95% confidence level the t is:

alpha = 1 - 95% = 1 - 0.95 = 0.05

alpha / 2 = 0.05 / 2 = 0.025

now well for t alpha / 2 (0.025) and df (149) = t = 1,976

the margin of error = E = t * sd / (n ^ (1/2))

replacing:

E = 1,976 * 3.75 / (150 ^ (1/2))

E = 0.605

The 95% confidence interval estimate of the popilation mean is:

m - E <u <m + E

16.2 - 0.605 <u <16.2 + 0.605

15,595 <u <16,805

(15,595, 16,805)

5 0
3 years ago
Frank rode his bicycle for 4 miles on Saturday. How many yards did he ride his bicycle?
denis23 [38]

Answer:

7,040 yards

Step-by-step explanation:

there are 1,760 yards in a mile, so 1,760 multiplied by 4 is 7,040

7 0
3 years ago
I need help for question 17 in my big ideas math homework, it says "Use the figure to find the measures of the numbered angles."
Dafna1 [17]

Answer:

can you show a pic tell me in the comments

Step-by-step explanation:

7 0
3 years ago
If
Anna11 [10]
Answer: -104

Explanation: x=-9 y=2
2(y-3xy)
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Hope it helped

4 0
2 years ago
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