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3 years ago

PLEASEEEE HELP MEEEE IM FAILING MATH AND I DONT UNDERSTAND.

Mathematics

2 answers:

pentagon [3]3 years ago

7 0

There should be a proof in the text book that matches the one your working on, just copy the stuff into what you're working on.

earnstyle [38]3 years ago

3 0

Here is picture for this question=

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Prove that : cos10° - sin10° / sin10° + cos10° = tan35°

Digiron [165]

Step-by-step explanation:

(cos 10° − sin 10°) / (cos 10° + sin 10°)

Rewrite 10° as 45° − 35°.

(cos(45° − 35°) − sin(45° − 35°)) / (cos(45° − 35°) + sin(45° − 35°))

Use angle difference formulas.

(cos 45° cos 35° + sin 45° sin 35° − sin 45° cos 35° + cos 45° sin 35°) / (cos 45° cos 35° + sin 45° sin 35° + sin 45° cos 35° − cos 45° sin 35°)

sin 45° = cos 45°, so dividing:

(cos 35° + sin 35° − cos 35° + sin 35°) / (cos 35° + sin 35° + cos 35° − sin 35°)

Combining like terms:

(2 sin 35°) / (2 cos 35°)

Dividing:

tan 35°

3 0

3 years ago

At what point on the parabola y = 3x^2 + 2x is the tangent line parallel to the line<br> y = 10x −2?

oksian1 [2.3K]

Answer:

( $\frac{4}{3}$ , 8 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 10x - 2 ← is in slope- intercept form

with slope m = 10

Parallel lines have equal slopes

then the tangent to the parabola with a slope of 10 is required.

the slope of the tangent at any point on the parabola is $\frac{dy}{dx}$

differentiate each term using the power rule

$\frac{d}{dx}$ (a $x^{n}$ ) = na $x^{n-1}$ , then

$\frac{dy}{dx}$ = 6x + 2

equating this to 10 gives

6x + 2 = 10 ( subtract 2 from both sides )

6x = 8 ( divide both sides by 6 )

x = $\frac{8}{6}$ = $\frac{4}{3}$

substitute this value into the equation of the parabola for corresponding y- coordinate.

y = 3( $\frac{4}{3}$ )² + 2

= (3 × $\frac{16}{9}$ ) + 2

= $\frac{16}{3}$ + $\frac{8}{3}$

= $\frac{24}{3}$

= 8

the point on the parabola with tangent parallel to y = 10x - 2 is ( $\frac{4}{3}$ , 8 )

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2 years ago

Your brother is 13 your age. Your sister is 6 years older than your brother. Your sister is 10 years old. Write and solve an equ

Bogdan [553]

The brother is 4 years old

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3 years ago

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average i

strojnjashka [21]

The valid conclusions for the manager based on the considered test is given by: Option

<h3>When do we perform one sample z-test?</h3>

One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.

For this case, we're specified that:

Population mean = $\mu$ = $150
Population standard deviation = $\sigma$ = $30.20
Sample mean = $\overline{x}$ = $160
Sample size = n = 40 > 30
Level of significance = $\alpha$ = 2.5% = 0.025
We want to determine if the average customer spends more in his store than the national average.

Forming hypotheses:

Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get: $H_0: \mu_0 \leq \mu = 150$
Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically $H_1: \mu_0 > \mu = 150$